Theoretical and Methodological Issues in Research on Teachers’ Beliefs

1. Theoretical and Methodological Issues in Research on Teachers’ Beliefs Keith R. Leatham Brigham Young University Denise S. Mewborn University of Georgia Natasha M. Speer Michigan State University 2006 NCTM Research Pressession

2. Presentation Outline • Beliefs as a Lever for Change—Denise • Viewing Teachers’ Beliefs as Sensible Systems—Keith • Inconsistencies in beliefs and practices: Methodological artifact?—Natasha • Discussion 2006 NCTM Research Pressession

3. Beliefs as a Lever for Change Denise S. Mewborn University of Georgia 2006 NCTM Research Pressession

4. Carrie • I hate math. Math was invented by someone who was very angry as a way to get back at society. And the thought of teaching math wakes me up in the middle of the night in a cold sweat. 2006 NCTM Research Pressession

5. Carrie, 6 months later • Teaching math is nothing more than exploring math with your learners. I’ve learned that “wrong answers” are such a gift in the classroom because they open the doors for so much more understanding and exploration of math. 2006 NCTM Research Pressession

6. Explaining change • Abundance of studies that show no change • Few studies that explain change 2006 NCTM Research Pressession

7. My claim • Explain change by looking at both the structure and the content of a system of beliefs 2006 NCTM Research Pressession

8. Green (1971) • Primary vs. derivative primary primary der der der der der der 2006 NCTM Research Pressession

9. Core vs. peripheral peripheral core 2006 NCTM Research Pressession

10. Clusters • Evidentially-held vs. nonevidentially-held 2006 NCTM Research Pressession

11. Green’s ideal belief system • Minimum number of core beliefs • Minimum number of clusters • Maximum proportion of evidential beliefs • Primary-derivative structure is logical • Conclusion: We have much work to do here. 2006 NCTM Research Pressession

12. Carrie’s beliefs about mathematics • Not creative (left brain vs. right brain) • Not coherent (mathematics vs. language arts) • Difficult, frustrating, humiliating • Evidentially-held based on personal experience 2006 NCTM Research Pressession

13. Carrie’s core belief • Care ethic • Children as people who need to be respected • School as a safe place–physically, intellectually & emotionally • “Celebrating children” 2006 NCTM Research Pressession

14. Carrie’s derivative beliefs • Students • Value their thinking • Boost their self-confidence • Learn to be a better person • Learning • Process, not product • Teaching • Teacher as role model 2006 NCTM Research Pressession

15. Structure: Preservice teaching math celebrating children students learning 2006 NCTM Research Pressession

16. Explaining change • Carrie was aware of and could articulate the conflicting clusters of beliefs • Teacher education built on Carrie’s core belief • Teacher education challenged Carrie’s beliefs about mathematics • Beliefs about mathematics were held evidentially–teacher education provided new evidence • Carrie subsumed mathematics cluster into main cluster of beliefs 2006 NCTM Research Pressession

17. Structure revisited celebrating children teaching learning students math math math 2006 NCTM Research Pressession

18. Content of Carrie’s beliefs • Confirms much earlier literature • No new information from a research perspective • No viable avenues for change from a teaching perspective 2006 NCTM Research Pressession

19. Structure of Carrie’s beliefs • Really not possible to look at structure alone • Determining primary and derivative beliefs requires examination of content • Again, no viable explanation of change from looking at structure only 2006 NCTM Research Pressession

20. Combining structure & content • Levers for change • Promote self-awareness of beliefs • Determine core belief-must be affirmed • Lever for resolving apparent inconsistencies • Look at wider set of beliefs • Determine what counts as evidence • Lever for presenting perturbations • Research inroads 2006 NCTM Research Pressession

21. Implications/Questions • Under what conditions are beliefs less resistant to change? • Under what conditions can change be more rapid? • Look at beliefs in wider context than mathematics–how wide? 2006 NCTM Research Pressession

22. Is Carrie a special case? • Yes • Aware of inconsistencies • Seeking answers • Not necessarily • How many Carries have I missed because I saw only the content of their beliefs? • Structure of beliefs made her a prime candidate for change 2006 NCTM Research Pressession

23. Methodological considerations • Deliberate efforts to uncover structure • Push for connections and related ideas • Widen the focus 2006 NCTM Research Pressession

24. Viewing Teachers’ Beliefs as Sensible Systems Keith R. Leatham Brigham Young University 2006 NCTM Research Pressession

25. It will not be possible for researchers to come to grips with teachers’ beliefs… without first deciding what they wish belief to mean and how this meaning will differ from that of similar constructs. Pajares Defining Belief 2006 NCTM Research Pressession

26. Defining Belief • “All beliefs are predispositions to action.” Rokeach • one need not be able to articulate that belief, nor even be consciously aware of it • A belief “speaks to an individual’s judgment of the truth or falsity of a proposition.” Pajares • the proposition is often implicit 2006 NCTM Research Pressession

27. Coherence Theory Coherentism signifies the view that would seek to explain meaning, knowledge, and even truth by reference to the interrelationships between assorted epistemically salient elements. Alcoff A belief is justified to the extent to which the belief-set of which it is a member is coherent. Dancy 2006 NCTM Research Pressession

28. Coherence Theory Our knowledge is not like a house that sits on a foundation of bricks that have to be solid, but more like a raft that floats on the sea with all the pieces of the raft fitting together and supporting each other. A belief is justified not because it is indubitable or is derived from some other indubitable beliefs, but because it coheres with other beliefs that jointly support each other. Thagard 2006 NCTM Research Pressession

29. Sensible Systems of Beliefs • Green’s Metaphor with Coherentism • Psychological strength • The strength of a belief depends on how that belief coheres with the rest of the belief system. • Quasi-logical relationships • One reason we may posit the existence of a quasi-logical relationship is a desire (often subconscious) to make two beliefs more coherent when considered in tandem. • Isolated clusters • Contextualization facilitates the coherence of seemingly inconsistent beliefs. 2006 NCTM Research Pressession

30. Sensible Systems of Beliefs • As researchers it is often difficult to look beyond the beliefs we assume must have been (or should have been) the predisposition for a given action. • Observations of seeming contradictions are, in the language of constructivism, perturbations, and thus an opportunity to learn. • Teacher actions neither prove nor disprove our belief inferences. 2006 NCTM Research Pressession

31. The Case of Joanna Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher's mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28, 550-576. • Traditional beliefs about mathematics • Primarily nontraditional beliefs about learning and teaching mathematics • Primarily traditional practice 2006 NCTM Research Pressession

32. The Case of Joanna “Joanna’s model shows factors, such as time, constraints, scarcity of resources, concerns over standardized testing, and students’ behavior, as potential causes of inconsistency. These represent competing influences on practice that are likely to interrupt the relationship between beliefs and practice.” 2006 NCTM Research Pressession

33. The Case of Joanna through the Sensible System Lens Joanna’s beliefs about the importance of standardized testing and about the need to control students’ behavior were more centrally held and thus had greater influence on her mathematics teaching than her beliefs about learning mathematics. 2006 NCTM Research Pressession

34. The Case of Fred Cooney, T. J. (1985). A beginning teacher's view of problem solving. Journal for Research in Mathematics Education, 16, 324-336. • Mathematics is problem solving • Mathematics teaching should focus on problem solving • Practice was fairly procedural 2006 NCTM Research Pressession

35. The Case of Fred “His classroom practice was faithful to his previously espoused views, but the meaning he held for problem solving was limited, as was the means by which he could translate belief into practice.” 2006 NCTM Research Pressession

36. The Case of Fred through the Sensible System Lens Fred’s core belief about mathematics was that mathematics is interesting in its own right. It appears that Fred used “problem solving” as a catchword associated with what he enjoyed about doing mathematics. Motivating students to engage in mathematics was getting them to “problem solve.” This belief about “problem solving” significantly influenced his teaching practice. 2006 NCTM Research Pressession

37. The Case of Christopher Skott, J. (2001). The emerging practices of a novice teacher: The roles of his school mathematics images. Journal of Mathematics Teacher Education, 4, 3-28. • Mathematics is about experimenting and investigating • Teaching mathematics should be about inspiring independent student learning • Action: Mathematics-depleting questioning 2006 NCTM Research Pressession

38. The Case of Christopher “[This action] should not be seen as a situation that established new and contradictory priorities, but rather as one in which the energising element of Christopher’s activity was not mathematical learning. He was, so to speak, playing another game than that of teaching mathematics.” 2006 NCTM Research Pressession

39. The Case of Christopher through the Sensible System Lens When time began to be an issue, the more centrally held belief for Christopher was his belief in the importance of individuals and their need to feel successful. The importance of this belief meant mathematical beliefs sometimes took a back seat. 2006 NCTM Research Pressession

40. The Case of Jeremy “I plan to involve all students in technology.” “It is necessary to use technology in all mathematics above and including at least Algebra I.” 2006 NCTM Research Pressession

41. The Case of Jeremy “Like pre-algebra and the general math, I don’t know much about that. I don’t have very much exposure…. No matter what level I’m teaching,… it doesn’t matter; I would like to use [technology]…. So, in that sense, it doesn’t depend on what level… I’m teaching. And then, “Are there topics where you think that it is necessary?” I think it’s necessary above Algebra I.” 2006 NCTM Research Pressession

42. The Case of Jeremy “In my class I will consider [technology] necessary, because I’ve seen how it can help you learn and I think that anything that can be used to help students learn is necessary for good learning.” 2006 NCTM Research Pressession

43. The Case of Jeremy through the Sensible System Lens Quasilogical relationship: As a teacher, it is necessary that I use any method I know to be effective to help students learn mathematics. I know technology is an effective way to help students learn (from Algebra I on up). Therefore, it is necessary that I use technology in my teaching (from Algebra I on up). 2006 NCTM Research Pressession

44. Implications for Research • Search for meaning through search for coherence. Seek to develop models of sensible systems. • The broader our scope, the more likely we are to find critical, centrally held beliefs 2006 NCTM Research Pressession

45. Implications for Teacher Education • Goal of teacher education? • Need to connect mathematics specific and general beliefs about education. Seek for connection rather than isolation in mathematics education. • Move reform-oriented beliefs about mathematics, its teaching and learning to a more centrally located position in teachers’ belief systems. 2006 NCTM Research Pressession

46. Teachers make sense. Keith R. Leatham Brigham Young University kleatham@mathed.byu.edu 2006 NCTM Research Pressession

47. Inconsistencies in beliefs and practices: Methodological artifact? Natasha Speer Michigan State University 2006 NCTM Research Pressession

48. Research has demonstrated that beliefs ARE evident in • instructional practices (Calderhead, 1996; Thompson, 1992) • teacher development and change in preparation and professional development programs (Fennema & Scott Nelson, 1997; Richardson, 1996) 2006 NCTM Research Pressession

49. Research has demonstrated that beliefs are NOT evident in: • instructional practices (Cohen, 1990; Thompson, 1984) • teacher development and change in preparation and professional development programs (Borko & Putnam, 1996; Sykes, 1990) 2006 NCTM Research Pressession

50. Inconsistencies are sometimes apparent when we… • Gather data on (1) beliefs teachers state or profess (2) beliefs researchers attribute to teachers (from data on their instructional practices) • Compare and contrast findings from (1) and (2) 2006 NCTM Research Pressession